Best Known (184, 184+33, s)-Nets in Base 4
(184, 184+33, 16384)-Net over F4 — Constructive and digital
Digital (184, 217, 16384)-net over F4, using
- net defined by OOA [i] based on linear OOA(4217, 16384, F4, 33, 33) (dual of [(16384, 33), 540455, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- OOA 16-folding and stacking with additional row [i] based on linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using
(184, 184+33, 87381)-Net over F4 — Digital
Digital (184, 217, 87381)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4217, 87381, F4, 3, 33) (dual of [(87381, 3), 261926, 34]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4217, 262143, F4, 33) (dual of [262143, 261926, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, 262144, F4, 33) (dual of [262144, 261927, 34]-code), using
- an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- discarding factors / shortening the dual code based on linear OA(4217, 262144, F4, 33) (dual of [262144, 261927, 34]-code), using
- OOA 3-folding [i] based on linear OA(4217, 262143, F4, 33) (dual of [262143, 261926, 34]-code), using
(184, 184+33, large)-Net in Base 4 — Upper bound on s
There is no (184, 217, large)-net in base 4, because
- 31 times m-reduction [i] would yield (184, 186, large)-net in base 4, but